求函数y=sin（x+π/6）+cosx,（0≤x≤π）的最大值和最小值

y=sin（x+π/6）+cosx
=sinxcos(π/6)+cosxsin(π/6)+cosx
=(√3/2)*sinx+(3/2)cosx
=√3*[(1/2)*sinx+(√3/2)cosx]
=√3*sin(x+π/3)
因为0≤x≤π,即π/3≤x+π/3≤4π/3
所以-√3/2≤sin(x+π/3)≤1
则当x+π/3＝π/2,即x＝π/6时,sin(x+π/3)＝1,函数y有最大值√3；
当x+π/3＝4π/3,即x＝π时,sin(x+π/3)＝-√3/2,函数y有最小值－3/2.